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If (t- 8) is a factor of t^2 - kt - 48, then k=

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If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 02:53
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Question Stats:

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

Problem Solving
Question: 57
Category: Algebra Second-degree equations
Page: 69
Difficulty: 600


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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 02:53
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SOLUTION

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

(t - 8) is a factor of t^2 - kt - 48 means that t = 8 is a solution of the equation t^2 - kt - 48 = 0.

Substitutet = 8 to get the value of k: 8^2 - 8k - 48 = 0 --> k = 2.

Answer: C.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 04:55
Factoring the expression:
(t - 8) (t - ?), since (t - 8) is a factor, the other bracket has to be (t + 6).
The net result is -2. So (B)? Not sure of the answer because I got lost with the signs a bit.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 22:27
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Put the value of t-8=0, or t=8 in equation t^2+kt+48=0: Solving we get k=2.
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 24 Jan 2014, 23:46
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If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(8) - 2
(C) 2
(0) 6
(E) 14


It is given that (t - 8) is a factor of the quadratic expression t^2 - kt - 48
Hence, we need to find the other factor of -48 such that the sum of factors is-k.

Thus, (-8) * x = -48

Or, x = 6

So, -k = (-8) + 6 = - 2

Or, k = 2

Answer: (C)
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 25 Jan 2014, 11:39
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SOLUTION

If (t- 8) is a factor of t^2 - kt - 48, then k=

(A) - 6
(B) - 2
(C) 2
(D) 6
(E) 14

(t - 8) is a factor of t^2 - kt - 48 means that t = 8 is a solution of the equation t^2 - kt - 48 = 0.

Substitutet = 8 to get the value of k: 8^2 - 8k - 48 = 0 --> k = 2.

Answer: C.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 25 Feb 2014, 18:44
-8 x ?? = -48
?? = 6, so the other factor is 6
(t-8)(t+6) would be the two factors
-k = -8+6
-k = -2
k=2 Answer = C
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k= [#permalink] New post 22 May 2014, 23:38
Vieta's formulas applied to quadratic: x1+x2= -b/a & x1*x2=c/a
From what is given in the question: 8+x2=k and 8*x2=-48
so, x2=-6 and thus 8-6=k i.e. k=2
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Re: If (t- 8) is a factor of t^2 - kt - 48, then k=   [#permalink] 22 May 2014, 23:38
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